The France international, 29, was dismissed for violent conduct after an incident with Augsburg’s Korean international Ja-cheol Koo early in the second half.
Koo reacted to a tackle by grabbing Ribery’s neck, with the former Marseille man responding by pushing his opponent in the face.
Ribery will miss the quarter-final clash with Borussia Dortmund in late February.
The club accepted the sanction, although there was a difference of opinion between its senior staff members.
Coach Jupp Heynckes said “it was a justified red card as, while he was provoked, a player of his class should not react this way”.
But chairman Karl Heinz Rummenigge said both players should have been booked and no more.
“Obviously it should not have been a red card – Franck reacted to the Korean’s action, and it’s impossible that he should be dismissed and the other not even see a yellow card.”